Several anime series (I would say half of them) do a Title Drop on the last episode: the final episode's title is the same as the series'.
Around when did it become so commonplace, and what are the reasons for the showmakers to do so?
This trope's origins don't lie in anime. An early example of a title drop in film is 1929's "All Quiet on the Western Front", or even earlier in the Sherlock Holmes novel "A Study in Scarlet" (1887). Generally title drops are done near the end of a work in order to give the desired effect of new understanding of the title with the context of the story.
The first known japanese animation ever created was in 1907's 13 second long "Katsudo Shashin", so the trope pre-dates anime history.
By the time anime was being televised (1960s), this trope was a staple feature in many media formats, so it's not a surprise that it transferred itself into anime also.
Bear in mind that many anime are adaptions from light novels, manga and other formats, so the title drops may be transferred from there.